There are generally two possible reasons why you cannot empty
ShortPixel Image Optimizer‘s backup folder:
- The backed up files do not have the correct permissions and/or ownership. This can happen when the website is moved from one hosting provider to another: The permissions may be kept, but the ownership of the files may be the old one, so the images won’t be able to be removed. Contact your hosting provider directly and ask them to either remove the files for you or set the proper permissions and ownership for the backed up files.
- There are many images in a backup folder and the plugin times out when trying to remove them. A solution that usually works is to install the WPTerm plugin and then from the command line simply go into the backup folder and remove all the files as in the example below.
Please do this only if you are familiar with the command line. 
Alternatively, you can always contact your hosting provider and ask them to help you with this.